Accelerated SPECT Monte Carlo Simulation using Multiple Projection Sampling and Convolution-based Forced Detection

Monte Carlo (MC) is a well utilized tool for simulating photon transports in single photon emission computed tomography (SPECT) due to its capability for high accuracy. As a consequence of this accuracy, it suffers from a relatively low detection efficiency, and thus long computation times. One technique used to improve the speed of MC modeling is the effective and well established variance reduction technique (VRT) known as forced detection (FD). With this method, photons are followed as they transverse the object under study, but are then forced to travel in the direction of the detector surface whereby they are convolved with a $\delta$ function determined from the probability density function (PDF). Another more sufficient method called convolution-based forced detection (CFD) is based upon the fundamental idea of FD with the exception that detected photons are rather convolved with a distance-dependent blurring kernel. In order to further increase the speed of MC, a method named multiple projection convolution-based forced detection (MP-CFD) is presented. Rather than forcing photon to hit a single detector, the MP-CFD method follow the photon transport through the object, but then at each scatter site, forces the photon to interact with the detectors at a variety of angles surrounding the object. In this way, it is possible to simulate all the projection images in SPECT simulation simultaneously, rather than as separate projections. The result of this is vastly improved simulation times as much of the computation load of simulating photon transport through the object is done only once for all projection angles. The results of MP-CFD agree well with the experimental data in measurements of point spread function (PSF's), with correlation coefficiant $(r^{2})$ as 0.997. The speed of MP-CFD is shown to be about 60 times faster than regular forced detection MC with similar result.